Plicker time!
Principles of Data Collection for Inference
case/observational unit - the individual unit on which you make observations (a row in a data frame) [In arbuthnot data set, case is year]
population - the target group of observational units about which you'd like to make inferences [size of the population: \(N\)]
sample - a subset of the population on which you have data [size of the sample: \(n\)]
anecdote - very small sample of data collected haphazardly [usually \(n = 1\)]
census - sample = population [complex, expensive, and sometimes impossible to achieve]
Cooking as Sampling
Sampling considerations
You're a senior Psychology major conducting a study that examines procrastination among Reed students. How should you select a sample?
-
Post a link to your survey on your Facebook page
- \(n \approx 400\)
-
Get a list of Reed student emails from the Registrar, take a simple random sample (SRS), and email that sample
- Initial \(n = 100\), Final \(n = 34\)
Landon v. FDR, 1936
Literary Digest polled 10 million Americans, 2.4 million responded.
\(N = 128\) million, \(n = 2.4\) million
Prediction: 43% for FDR
Result: 62% for FDR
What went wrong?
Literary Digest surveyed
- magazine subscribers
- registered car owners
- registered telephone owners
These groups have a much higher income on average than the typical american. In 1936 the Great Depression is still in full swing, so the typical (poorer) american was more supportive of FDR.
Their sampling method was biased (not representative).
Lesson
Getting a representative sample is much more important than a large sample.